Due to the wide diffusion of JPEG coding standard, the image forensic community has devoted significant attention to the development of double JPEG (DJPEG) compression detectors through the years. The ability of detecting whether an image has been compressed twice provides paramount information toward image authenticity assessment. Given the trend recently gained by convolutional neural networks (CNN) in many computer vision tasks, in this paper we propose to use CNNs for aligned and non-aligned double JPEG compression detection. In particular, we explore the capability of CNNs to capture DJPEG artifacts directly from images. Results show that the proposed CNN-based detectors achieve good performance even with small size images (i.e., 64x64), outperforming state-of-the-art solutions, especially in the non-aligned case. Besides, good results are also achieved in the commonly-recognized challenging case in which the first quality factor is larger than the second one.